Functions for generating guessed sets of true null hypotheses in empirical Bayes resampling-based multiple hypothesis testing
These functions are called internally by the main user-level function EBMTP. They are used for estimating local q-values, generating guessed sets of true null hypotheses, and applying these results to function closures defining the choice of type I error rate (FWER, gFWER, TPPFP, and FDR).
Hsets(Tn, nullmat, bw, kernel, prior, B, rawp) ABH.h0(rawp) G.VS(V, S = NULL, tp = TRUE, bound)
Tn |
The vector of observed test statistics. |
nullmat |
The matrix of null test statistics obtained either through null transformation of the bootstrap distribution or by sampling from an appropriate multivariate normal distribution (when |
bw |
A character string argument to |
kernel |
A character string argument to |
prior |
Character string indicating which choice of prior probability to use for estimating local q-values (i.e., the posterior probabilities of a null hypothesis being true given the value of its corresponding test statistic). Default is 'conservative', in which case the prior is set to its most conservative value of 1, meaning that all hypotheses are assumed to belong to the set of true null hypotheses. Other options include 'ABH' for the adaptive Benjamini-Hochberg estimator of the number/proportion of true null hypotheses, and 'EBLQV' for the empirical Bayes local q-value value estimator of the number/proportion of true null hypotheses. If 'EBLQV', the estimator of the prior probability is taken to be the sum of the estimated local q-values divided by the number of tests. Relaxing the prior may result in more rejections, albeit at a cost of type I error control under certain conditions. See references. |
B |
The number of bootstrap iterations (i.e. how many resampled data sets) or the number of samples from the multivariate normal distribution (if |
rawp |
A vector of raw (unadjusted) p-values obtained bootstrap-based or influence curve null distribution. |
V |
A matrix of the numbers of guessed false positives for each cut-off, i.e., observed value of a test statistic, within each sample in |
S |
A matrix of the numbers of guessed true positives for each cut-off, i.e., observed value of a test statistic, within each sample in |
tp |
Logical indicator which is TRUE if type I error rate is a tail probability error rate and FALSE is if it is an expected value error rate. |
bound |
If a tail probability error rate, the bound to be placed on function of guessed false positives and guessed true positives. For, 'fwer', equal to 0; 'gfwer', equal to 'k'; and tppfp, equal to 'q'. |
The most important object to be returned from the function Hsets is a matrix of indicators, i.e., Bernoulli realizations of the estimated local q-values, taking the value of 1 if the hypothesis is guessed as belonging to the set of true null hypotheses and 0 otherwise (guessed true alternative). Realizations of these probabilities are generated with a call to rbinom, meaning that this function will set the RNG seed forward another B*(the number of hypotheses) places. This matrix, with rows equal to the number of hypotheses and columns the number of (bootstrap or multivariate normal) samples is used to subset the matrix of null test statistics and the vector of observed test statistics at each round of (re)sampling into samples of statistics guessed as belonging to the sets of true null and true alternative hypotheses, respectively. Using the values of the observed test statistics themselves as cut-offs, the numbers of guessed false positives and (if applicable) guessed true positives can be counted and eventually used to estimate the distribution of a type I error rate characterized by the closure returned from G.VS. Counting of guessed false positives and guessed true positives is performed in C through the function VScount.
For the function Hsets, a list with the following elements:
Hsets.mat |
A matrix of numeric indicators with rows equal to the number of test (hypotheses, typically |
EB.h0M |
The estimated proportion of true null hypotheses as determined by nonparametric density estimation. This value is the sum of the estimated local q-values divided by the total number of tests (hypotheses). |
prior |
The value of the prior applied to the local q-value function. If 'conservative', the prior is set to one. Otherwise, the prior is the value obtained from the estimator of the adaptive Benjamini-Hochberg procedure (if |
pn.out |
The vector of estimated local q-values. This vector is returned in the |
For the function ABH.h0, the estimated number of true null hypotheses using the estimator from the linear step-up adaptive Benjamini-Hochberg procedure.
For the function G.VS, a closure which accepts as arguments the matrices of guessed false positive and true positives (if applicable) and applies the appropriate function defining the desired type I error rate.
Houston N. Gilbert
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set.seed(99) data<-matrix(rnorm(90),nr=9) group<-c(rep(1,5),rep(0,5)) #EB fwer control with centered and scaled bootstrap null distribution #(B=100 for speed) eb.m1<-EBMTP(X=data,Y=group,alternative="less",B=100,method="common.cutoff") print(eb.m1) summary(eb.m1) par(mfrow=c(2,2)) plot(eb.m1,top=9) abh <- ABH.h0(eb.m1@rawp) abh eb.m2 <- EBupdate(eb.m1,prior="ABH") eb.m2@prior
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